Definition:Normal Extension/Definition 2
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Definition
Let $L / K$ be a field extension.
Let $\overline K$ be the algebraic closure of $K$.
Let $\Gal {L / K}$ denote the set of embeddings of $L$ in $\overline K$ which fix $K$ pointwise.
Then $L / K$ is a normal extension if and only if:
- $\map \sigma L = L$
for each $\sigma \in \Gal {L / K}$.